First, if you are not qualified to walk, and your grades are excellent, or the university has won many awards because of many practical projects, it is difficult for you to impress the teacher by writing emails, and the teacher is usually very busy and will only give a formulaic answer to welcome to the exam, so writing emails before the postgraduate entrance examination is basically meaningless and a waste of time. Of course, if you want to consult the teacher's enrollment quota and exam materials, it is also possible.
Second, it is generally better to contact the tutor after the exam. Why don't you write an email and meet face to face? There is no point in communicating by email. Only by meeting can the teacher get to know you. But in Tsinghua, there are usually several teachers in the tutor group to meet a student, so you can't know whether the tutor you are looking for will appear in the second interview or how much decision he has! Therefore, it is almost impossible to ensure that you are 100% admitted by looking for a tutor. Of course, you just want to talk to the teacher, and it's no problem to give some professional and retest advice.
Thirdly, I know a lot of children's shoes that were admitted to Tsinghua together, and 80% or 90% of them have never seen a teacher or written an email. So don't think too much, just concentrate on reviewing. Strength is everything. Generally speaking, the school teachers are fair.
Of course, the situation of each school is different, for reference only.
If you really want to write an email to express your interest in his research direction, you'd better check his introduction, study his published articles and talk about his direction and articles. Then you can tell him yourself, your strengths. Conditional appointment is the best!
I wish the postgraduate entrance examination a success!